Answer:
[tex] ln(x) (\frac{x^2}{2}-x) - \frac{x^2}{4} + x + c[/tex]
Step-by-step explanation:
We will use the parts method of integration. ln(x) can be derivated while we integrate the polynomium x-1.
Thus,
[tex]\int (x-1)ln(x) \, dx = ln(x)(\frac{x^2}{2} - x) - \int \frac{\frac{x^2}{2} - x}{x} \, dx = ln(x)(\frac{x^2}{2} - x) \int \frac{x}{2}-1 \, dx =\\ln(x) (\frac{x^2}{2}-x) - (\frac{x^2}{4}-x + k) = ln(x) (\frac{x^2}{2}-x) - \frac{x^2}{4} + x + c[/tex]
